This paper considers the combined problems of railroad blocking, train design and train assignment as observed in the railroad industry. The problem of railroad blocking deals with finding the least cost paths for a given set of shipments over an entire railroad network. Blocking is defined as an activity where a set of shipments arriving at or commencing from a certain node station and departing to another particular node station, or further, are grouped together and sent across as the same train to minimize costs and exploit economies of scale. This problem has marked similarities with the airline scheduling which operates flights across a predetermined hub and spoke network. The problem considered here not only necessitates determining the “right” hubs and “right” trains to be scheduled on the network, but also scheduling the shipments on appropriate trains between the hub station yards and spoke station yards so that the overall costs are minimized.

There are a large number of practical and logical constraints associated with the problem. Apart from the capacity related constraints on the arcs, nodes and trains as observed in prior literature, it is required that the trains run only on crew segments, which act as the transit nodes for crew members. The main objective of our efforts would be to find a cost minimizing set of feasible trains that operate entire on crew segments. Our algorithm will also determine the least cost assignment of shipments to these trains. The results of our method are validated and reported for two real-life problem instances and demonstrate the advantage of using a joint mixed integer mathematical formulation over greedy heuristics that have largely been employed for this problem in literature.